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Recovering edge flow from Push-relabel
By Sorting, history, 4 years ago, In English

Is it possible to recover the flow for each edge after running the Push-relabel algorithm on a graph?

It seems like some inside cycles of flow can exist after running the algorithm.

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4 years ago, hide # |
 
Vote: I like it +36 Vote: I do not like it

There is some optimization for the push-relabel algorithm which only guarantees the answer to be preflow, not actual flows. To recover the solution, you should run flow decomposition or just get rid of this optimization. I think flow decomposition can be slow, so you should just generally don't have this optimization.

Here is the implementation without that optimization.

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    4 years ago, hide # ^ |
     
    Vote: I like it +29 Vote: I do not like it

    I was just reading through the implementation, and read a comment in it that said basic_string is bad for this specific use-case. Any idea why that might be the case (I've never faced any issue with using basic_string for graphs — weighted or unweighted)?

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      4 years ago, hide # ^ |
       
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      Well, it did something unbelievable, but I don't remember what it was. I think you can look up for C++ documentation to guess what it is.

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    4 years ago, hide # ^ |
     
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    What's the complexity without the optimization? I'm thinking of just using Dinic instead.

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      4 years ago, hide # ^ |
       
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      Complexity remains same: $$$O(V^2 \sqrt E)$$$. Even without the optimization, HLPP is still fast enough empirically.

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